### GEORGE MASON
UNIVERSITY

DEPARTMENT OF MATHEMATICAL
SCIENCES

COLLOQUIUM

FEBRUARY 14, 2017

**Speaker: **
Jason McCullough, Rider University

**Title: ***
Rees-like Algebras and the Eisenbud-Goto Conjecture
*

**Abstract:**
Regularity is a measure of the computational complexity of a homogeneous ideal in a polynomial ring and thus also a projective variety. There are examples in which the regularity growth is doubly exponential in terms of the degrees of the generators but better bounds were conjectured for "nice" ideals. Together with Irena Peeva, I discovered a construction that overturned some of the conjectured bounds for "nice" ideals - including the long-standing Eisenbud-Goto conjecture. Our construction involves two new ideas that we believe will be of independent interest: Rees-like algebras and step-by-step homogenization. I'll explain the construction and some of its consequences.

**Time:** Tuesday, February 14, 2017, 11:00 - 11:50 a.m.

**Place:** Exploratory Hall, room 4106

**Refreshments** will be served at 10:30 a.m.

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491